Final answer:
The expression (2^3)^(1/2) simplifies to the square root of 2^3, which results in the square root of 8.
Step-by-step explanation:
To evaluate the numerical expression ((2 to the power of 3) to the power of one-half), we first need to clarify the base and the exponents. The base is 2, and it is raised to the power of 3, which gives us 23 or 2 x 2 x 2, which equals 8. Next, this result (8) is raised to the power of one-half. Taking a number to the power of one-half is equivalent to finding the square root of that number. Therefore, (23)1/2 is the same as the square root of 8.
To find the square root of 8, we could split it into its prime factors, which are 2 x 2 x 2, but the simplest way is to understand that the square root of 8 simplifies to √2 x √4. Since the square root of 4 is 2, the answer becomes 2√2. But for our multiple-choice problem, we can look for the simplest form, which is the 'square root of 8' as one of the options provided.